After I gotten this equation, I tryed to excrete x1, but I'm missing one equation to make a state space model.
I think I need to get matrix A 4x4 and I don't know how to get x2 double derivate when it doesn't exist, if you know what I mean.

I think that state state space is effective by multiple input/output systems, but you have a system with only one input ( F ), thus a classical model is more effective here.
( And, yes, I have to admit that I have only limited experience with state space ).
When using the classical model, you can actually "see" what you are doing. In a 4x4 matrix, a certain number just disappears in the amount of numbers.

Say you have a closed loop (negative feed back).
Say that the forward path has the transfer function: A(s) and that the backward path has the transfer function: B(s), then Masons rule says that the transfer function for the loop as a whole =

Say you have a closed loop (negative feed back).
Say that the forward path has the transfer function: A(s) and that the backward path has the transfer function: B(s), then Masons rule says that the transfer function for the loop as a whole =
A(s) / ( 1 + A(s)*B(s) ) . . . . ( It's easy to prove ).
If the feedback is positive, you simply change the "+" to a "-".

Perhaps not too important for solving this task - but for the sake of clarity I like to mention that the given formula for the closed-loop transfer function is known as Blacks formula; Mason`s rule is different from that.
Questions:
* What is x2? Input or output (according to your block diagram)?
* Where is c1 in the diagram?

This is not right. By Laplace it could be written: k2*s*x2 = k2*s*x1 + c2(x1-x2) , and that's a 1. order system. A spring and a mass will oscillate which means that the system must be a 2. order system. You may not assume a mass (A), when it is not there.

In the (half) model in #8, you must complete the model. Then you can see what you are doing. Complete it and reduce it.

In #8 a force, F, is induced. Dividing this force by m you will get the acceleration of m: ( dx1/dt ). If you integrate this acceleration ( divide by s ) you will get x1.
The back-force ( as to F ) will be induced by: